XII HSC - BOARD
|
|
- Ferdinand Fletcher
- 5 years ago
- Views:
Transcription
1 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS Date: XII HSC - BOARD - 08 MATHEMATICS (40) - SOLUTIONS Q. (A) SECTION - I (i) If A 4, then adjoint of matri A is (A) 4 (A) (B) 4 (C) 4 (D) 4 A 4 adja 4 Topic: Matri; Sub-topic:Adjoint L- XII-HSC Board Test_Mathematics (ii) The principal solutions of sec are. (A), 6 (B) sec (B), 6 6 cos cos cos 6 6, 6 6 (C), 4 4 (D), 6 4 Topic: Trigo. function; Sub-topic:General solution_l- XII-HSC Board Test_Mathematics
2 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions (iii) The measure of acute angle between the lines whose direction ratios are,, 6 and,, is. (A) cos 7 (D) (B) cos 5 8 (C) cos (D) cos 8 cos cos 8 Topic: D Geometry; Sub-topic:Angle L- XII-HSC Board Test_Mathematics Q. (B) (i) Wirte the negations of the following statements : (a) (b) All students of this college live in the hostel. 6 is an even number or 6 is a perfect square. (a) p : All students of this college live in the hostel. Negation : p : Some students of this college do not live in the hostel. (b) p : 6 is an even number. q : 6 is a perfect square. Symbolic form : p q p q p q Negation : 6 is not an even number and 6 is not a perfect square. Topic: Logic; Sub-topic:Negation L- XII-HSC Board Test_Mathematics (ii) If a line makes angles,, with the co-ordinates aes, prove that cos cos cos 0. L.H.S : cos cos cos cos cos cos cos cos cos 0 = R.H.S Topic:D Geometry; Sub-topic: D L- XII-HSC Board Test_Mathematics
3 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions (iii) Find the distance of the point (,, ) from the plane y 4z 0 0. Distance of the point D a by cz d a b c y z,, a, b, c 4 y z to plane a by cz d 0 is D units 4 6 Topic:Plane; Sub-topic:Distance L- XII-HSC Board Test_Mathematics (iv) Find the vector equation of the lines which passes through the point with position vector 4iˆ ˆj kˆ and is in the direction of iˆ ˆj kˆ. Let a 4iˆ ˆj kˆ b ˆ i ˆj kˆ Equation of the line passing through point r a b 4ˆ ˆ ˆ ˆ ˆ ˆ Aa and having direction b is r i j k i j k Topic:Line; Sub-topic:Equation L- XII-HSC Board Test_Mathematics (v) If a iˆ ˆj 7 kˆ, b 5iˆ ˆj kˆ and c iˆ ˆj kˆ then find a b c. a b c a b c a b c a b c a b c 7 a b c 5 = ( + ) + ( 5 + ) +7(5 ) = = 5 Topic: Vector; Sub-topic:Triple dot product L- XII-HSC Board Test_Mathematics
4 Q. (A) (i) Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions Using vector method prove that the medians of a triangle are concurrent. Let a,b,c,d,e the position vectors of the vertices A, B, C of ABC and d, e, f be the position vectors of the midpoints D, E, F of the sides BC, CA and AB respectively A F G E B D C Then by the midpoint formula, b c, c a, a d e f b d b c ; e c a ; f a b d a a b c e b a b c f c a b c d a e b f c a b c g lies on the three medians AD, BE and CF dividing each of them internally in the ratio :. Hence, the medians are concurrent at point G. let Topic: Vector; Sub-topic:Theorem L- XII-HSC Board Test_Mathematics (ii) Using the truth table, prove the following logical equivalence : p q p q p q Mark Mark 4 A B 8 p q A B By column number and 8 p q p q p q Topic: Logic; Sub-topic:Truth table L- XII-HSC Board Test_Mathematics 4 4
5 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions (iii) If the origin is the centroid of the triangle whose vertices are A(, p, ), B(q,, 5) and R( 5,, r), then find the values of p, q, r. Let a, b, c be the position vectors of ABC whose vertices are A(, p, ), B(q,, 5), C( 5,, r) a iˆ pj ˆ kˆ, b qiˆ ˆj 5 kˆ, c 5iˆ ˆj rkˆ Given that origin O is the centroid of ABC a b c O a b c O iˆ pj ˆ kˆ qj ˆ ˆj 5kˆ 5iˆ ˆj rkˆ O q 5i ˆ p ˆ j 5 r k ˆ 0i ˆ 0 ˆ j 0k ˆ by equality of vectors q 5 0 q p 0 p 5 r 0 r p, q and r Topic:Vector; Sub-topic:Section formula L- XII-HSC Board Test_Mathematics Q. (B) (i) Show that a homogeneous equation of degree two in and y, i.e., a hy by 0 represents a pair of lines passing through the origin is h ab 0. Consider a homogenous equation of degree two in and y a hy by 0... i In this equation at least one of the coefficients a,b or h is non zero. We consider two cases Case I : If b = 0, then the equation of lines = 0 and (a + hy) = 0 These lines passes through the origin. Case II : b 0, Multiplying both the sides of equation (i) by b, we get ab hby b y 0 b y hby ab To make L.H.S a complete square, we add h on both the sides. b y hby h ab h by h h ab by h h ab by h h ab 0 by h h ab by h h ab 0 5 5
6 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions It is the joint equation of two lines i.e. by h h ab 0 and by h h ab 0 h h ab by 0 and h h ab by 0 These lines passes through the origin. Topic: Pair of straight line; Sub-topic:Theorem L- XII-HSC Board Test_Mathematics C A c a B (ii) In ABC, prove that tan cot. c a In ABC, by sine Rule, a b c k sin A sin B sin C a k sin A, b k sin B, c k sin C Consider, c a k sin C k sin A c a k sin C k sin A sin C sin A sin C sin A C A C A cos sin C A C A sin cos cot C A tan C A tan B tan C A tan C A C a cot B C a Hence proved. Topic: Trigo. function; Sub-topic:Theorem L- XII-HSC Board Test_Mathematics 6 6
7 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions (iii) Find the inverse of the matri, A 0 0 using elementary row transformations. A A eists. We know, AA I A R R R A R R R A R R R and R R R A R R R A A 5 Topic: Matri; Sub-topic:Inverse L- XII-HSC Board Test_Mathematics 7 7
8 Q. (A) (i) Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions Find the joing equation of the pair of lines passing through the origin, which are perpendicular to the lines represented 5 y y 0. Given homogeneous equation is 5 y y 0 Which is factorisable 5 5y y y 0 5 y y y 0 y y 5 0 y 0 and 5 y 0 are the two lines represented by the given equation. Their slopes are and 5 Required two lines are respectively perpendicular to these lines. Slopes of required lines are and Their individual equations are y and y 5 and the lines pass through origin. 5 i.e., y 0 and 5y 0 Their joint equation is y y 5 0 y 5y 5y 0 y 5y 0 Topic: Pair of straight line_sub-topic:formulation of equation L- XII-HSC Board Test_Mathematics (ii) Find the angle between the lines y z and 4 8 Let a and b be the vectors in the direction of the lines respectively. a 4 i j 8k and b iˆ j k y z 4. y z and 4 8 y z 4 a b and a b Let be the acute angle between the two given lines 8 8
9 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions a b 8 cos a b 9 cos Topic: Line; Sub-topic:Line L- XII-HSC Board Test_Mathematics (iii) Write converse, inverse and contrapositive of the following conditional statement : If an angle is a right angle then its measure is 90. Converse : If the measure of an angle is 90 then it is a right angle. Inverse : If an angle is not a right angle then its measure is not 90. Contra positive : If the measure of an angle is not 90 then it is not a right angle. Topic:Logic; Sub-topic:Condictional L- XII-HSC Board Test_Mathematics Q. (B) 56 (i) Prove that : sin cos sin 5 65 Let cos and let cos 5 sin sin y 5 sin y 5 4 cos y 5 using sin y sin cos y cos sin y y sin cos sin sin 5 65 Hence proved. Topic: Trigo. function; Sub-topic:ITF L- XII-HSC Board Test_Mathematics 9 9
10 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions (ii) Find the vector equation of the plane passing through the points A(, 0, ), B(,, ) and C(4,, ). Let the p.v. of points A(, 0, ), B(,, ) and C(4,, ) be a i k, b i j k and c 4i j k b a j, c a i j k i j k 0 0 b a c a i k Equation of plane through A, B, C in vector form is r a b a c a 0 r a i j 0 r i j i k i j r i j Topic: Plane; Sub-topic:Equation of plane L- XII-HSC Board Test_Mathematics (iii) Minimize Z = 7 + y subject to 5 y 5, y, 0, y 0 Z 7 y Subject to 5 y 5 y 0, y 0 Line Inequation Points on Points on y Feasible region AB 5 y 5 A,0 B 0,5 Non - origin side CD y unit = cm both ais C,0 D0, Non - origin side 0 0
11 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions B(0, 5) 5 D(0, ) P, P A(, 0) AB C(, 0) CD common feasible region BPC Points Minimize z 7 y B 0,5 Z B P 5, 5 5 Z P 7 6 C,0 Z C 7 0 Z is minimum at = 0, y = 5 and min (z) = 5 Topic: LPP; Sub-topic:Graphical solution L- XII-HSC Board Test_Mathematics SECTION - II Q.4 (A) Select and write the appropriate answer from the given alternatives in each of the following (i) sub-questions : [6] Let the p. m. f. of a random variable X be P( ) for,0,, 0 0 otherwise Then E( X ) is. (A) (B) (C) 0 (D) (C) 0 4 p p P 0 Topic: Probability distribution; Sub-topic:Epected value L- XII-HSC Board Test_Mathematics
12 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions k (ii) If, 8 6 then the value of k is. 0 (A) (B) (C) 4 (D) 5 (A) I k 0 6 tan k 0 6 tan k tan 0 k k 4 Topic:Definite integral; Sub-topic:Definite integral L- XII-HSC Board Test_Mathematics dy (iii) Integrating factor of linear differential equation y log is. (A) (D) (B) (C) (D) dy y log P I. F e e log Topic: Diferential equation; Sub-topic:LDE L- XII-HSC Board Test_Mathematics
13 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions Q.4 (B) Attempt any THREE of the following : [6] cos sin (i) Evaluate : e sin cos sin I e sin sin cot cosec cosec e f '( ) f ( ) e [ f ( ) f ( )] e f ( ) C I e cos ec C Topic: Integration; Sub-topic:Integration L- XII-HSC Board Test_Mathematics dy (ii) If y tan (log ), find. y [tan (log )] differentiate w.r.t. both side dy [tan (log )] sec (log ) dy 6 tan (log ) sec (log ) Topic: Differentiation; Sub-topic:Composite function L- XII-HSC Board Test_Mathematics (iii) Find the area of ellipse y. 4 Required area = 4 Area ( OAPB) 0 y y 4 y Required area 4 0 (0,) B O P (0,) A 8 sin 0
14 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions 8 0 sin () 0 8 sq.units Topic: Definite integral; Sub-topic:AOI L- XII-HSC Board Test_Mathematics (iv) Obtain the differential equation by eliminating the arbitrary constants from the following equation : y c e c e y c e c e differentiate w.r.t.. dy c e c e Again diff. w.r.t.. d y 4c e 4c e d y 4( c e c e ) 4 y 4y 0 Topic: Differential equation; Sub-topic:Formulation L- XII-HSC Board Test_Mathematics (v) Given X ~ B ( n, p) If n 0 and p 0.4, find E( X ) and Var. ( X ). n 0, p 0.4 q p 0.6 E( X ) np V ( ) npq Topic:Binomial distribution; Sub-topic:Mean L- XII-HSC Board Test_Mathematics 4 4
15 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions Q.5 (A) Attempt any TWO of the following: [6] (i) Evaluate: sin cos Let I sin cos Put tan t Then,, dt t t t sin and cos t t I dt /( t ) t t t t dt /( t ) ( ) 4 ( t t t ) dt t dt 4 4 ( ) t t t tan ( t ) c tan tan c Topic: Integration; Sub-topic:Method of substitution L- XII-HSC Board Test_Mathematics (ii) If a cos t, y asin t, show that We have, dy y dy dy / dt, / dt 0...() / dt Now, y a y asin t a (sin t) sin t dy d d a t a t t dt dt dt (sin ) (sin ) (sin ) a sin t cost...() Also, a acos t a(cos t) cost 5 5
16 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions d a t t dt dt cos (cos ) acos t ( sin t) a cos t sin t...() From (), () and (), dy a sin t cost sin t y a cos t sin t cost Topic:Differentiation; Sub-topic:Parametric function L- XII-HSC Board Test_Mathematics (iii) Eamine the continuity of the function: log00 log(0.0 ) f ( ) 00 for 0;at 0 f is continuous at 0 if lim f ( ) f (0) R.H.S. f (0)...(given)......() log00 log (0.0 ) log( 00 ) L.H.S. lim f ( ) lim lim [log( 00 )] 00 lim From () and (), L.H.S. = R.H.S. lim f ( ) f (0). 0 f is continuous at 0. Topic: Continuity; Sub-topic:At a point L- XII-HSC Board Test_Mathematics Q.5 (B) Attempt any TWO of the following: [8] (i) Find the maimum and minimum value of the function: f ( ) 6 0 f ( ) 6 0 f ( ) ( ) ( ) 6() ( 7 6) 6( )( 6) f has a maima/minima if f ( ) 0 i.e. if 6( )( 6) 0 i.e. if 0 or
17 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions i.e. if 0 or 6 Now, f ( ) 6( ) 4() 4 f () () 4 0 f () 0 Hence, f has a maimum at, by the second derivative test. Also, f (6) (6) 4 0 f (6) 0 Hence, f has a minimum at 6, by the second derivative test. Now, maimum value of f at, f () ( ) ( ) 6() and minimum value of f at = 6, f (6) (6 ) (6 ) 6() Topic: AOD; Sub-topic:Maima or Minima L- XII-HSC Board Test_Mathematics a (ii) Prove that: log a a a c a a a a a a a a a a a a a a log a log a c log a log a c a a a log a a c Topic: Integration; Sub-topic:Theorem L- XII-HSC Board Test_Mathematics 7 7
18 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions (iii) Show that: a a f ( ) f ( ), if f ( ) is an even function a 0 0, if f ( ) is an odd function We shall use the following results : b a a b f f...() b a b a f f t dt...() If c is between a and b, then b c b f f f...() a a c Since 0 lies between -a and a, by (), we have, a 0 a f f f I I... Say a a 0 In I, put t. Then dt When a, t a t a When 0, t 0 t f f t dt f t dt a a a a 0... f t dt By a 0... f By a a a a f f f 0 0 (i) If f is an even function, then f f in this case, a a a a a f f f f (ii) If f is an odd function, then f f in this case, a a a a a f f f f f 0. a Topic: Definite integral; Sub-topic:Theorem L- XII-HSC Board Test_Mathematics 8 8
19 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions Q.6 (A) Attempt any TWO of the following : [8] (i) If 9 f ( ), for 5, for, for is continuous at, find and. f is continuous at lim f ( ) lim f ()...() Now, 0 9 ( )( ) lim f ( ) lim lim ( ) 0 lim[( ) ] ( ) 6 lim ( ) lim () () f and Also, f () 5...(given) From (), we get, and and 5 7 and Topic: Continuity; Sub-topic:At a point L- XII-HSC Board Test_Mathematics (ii) Find dy if 5 y tan 6 Let 5 y tan tan 5 tan ( )( ) ( ) ( ) tan ( )( ) y Differentiate w.r.t. tan ( ) tan ( ) dy ( ) ( ) 9 9
20 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions Topic:Differentiation; Sub-topic:Inverse function L- XII-HSC Board Test_Mathematics (iii) A fair coin is tossed 9 times. Find the probability that it shows head eactly 5 times. Let X = no. of heads shows. n 9 p q ( ) n n.( ) n P X C p q X 0,,..., n P( X 5) C Topic:Binomial distribution; Sub-topic:Binomial distribution_l- XII-HSC Board Test_Mathematics Q.6 (B) Attempt any TWO of the following : [8] (i) Verify Rolle s theorem for the following function: f ( ) 4 0 on [0, 4] Since f ( ) is a polynomial, (i) It is continuous on [0, 4] (ii) It is differentiable on (0, 4) (iii) f (0) 0, f (4) f (0) f (4) 0 Thus all the conditions on Rolle s theorem are satisfied. The derivative of f ( ) should vanish for at least one point c in (0, 4). To obtain the value of c, we proceed as follows f ( ) 4 0 f ( ) 4 ( ) f ( ) 0 ( ) 0 c in (0, 4) We know that (0, 4) Thus Rolle s theorem is verified. Topic:AOD; Sub-topic:Roll s theorem L- XII-HSC Board Test_Mathematics
21 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions (ii) Find the particular solution of the differential equation: y( log ) log 0 dy when y e and e. Given equation is y( log ) log 0 dy y( log ) log dy y( log ) log dy Separating the variables, log dy y log Integrating, we have, log dy y log log y log log log c log y log c log y c log is the general solution. Given : e, y e e c e c. e.log e c. e. e y e log Topic:Differential equation; Sub-topic:Variable separable method_l-_xii-hsc Board Test_Mathematics (iii) Find the variance and standard deviation of the random variable X whose probability distribution is given below : P( X )
22 Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions p p p i i i i i i Total E( X ) pi i 8 Var( X ) p n i 9 4 i i 4 Var( X ) 4 Standard deivation of X 4 Topic: Probability distribution; Sub-topic:Epected value_l- XII-HSC Board Test_Mathematics
Rao IIT Academy/ ISC - Board 2018_Std XII_Mathematics_QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS. XII - ISC Board
Rao IIT Academy/ ISC - Board 8_Std XII_Mathematics_QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS XII - ISC Board MATHEMATICS - QP + SOLUTIONS Date: 6..8 Ma. Marks : Question SECTION - A (8 Marks)
More informationHSC - BOARD MATHEMATICS (40) - SOLUTIONS
Date: 8..5 Q. (A) SECTION - I (i) (d) A () (ii) (c) A A I 6 6 6 A I 64 I I A A 6 (iii) (a) fg cos A cos HSC - BOARD - 5 MATHEMATICS (4) - SOLUTIONS cos cos ch () hy g fy c...(i) Comparing with A Hy By
More informationBoard Answer Paper: MARCH 2014
Board Answer Paper: MARCH 04 and Statistics SECTION I Q.. (A) Select and write the correct answer from the given alternatives in each of the following: i. (C) Let l 0, m 3, n be the direction cosines of
More information22 (Write this number on your Answer Sheet)
Question Booklet Version (Write this number on your Answer Sheet) Day and Date : Thursday, 0th May, 08 QUESTION BOOKLET (MHT-CET - 08) Subjects : Paper I : Mathematics MH-CET 08 Roll No. Question Booklet
More informationRao IIT Academy/ 2015/ XII - CBSE - Board Mathematics Code(65 /2 /MT) Set-2 / Solutions XII - CBSE BOARD CODE (65/2/MT) SET - 2
Rao IIT Academ/ 5/ XII - CBSE - Board Mathematics Code(65 / /MT) Set- / Solutions XII - CBSE BOARD CODE (65//MT) SET - Date: 8.3.5 MATHEMATICS - SOLUTIONS. Let a iˆ 3iˆ kˆ b iˆ ˆj and a b 3 5, b a b Projection
More informationSUBJECT : PAPER I MATHEMATICS
Question Booklet Version SUBJECT : PAPER I MATHEMATICS Instruction to Candidates. This question booklet contains 50 Objective Type Questions (Single Best Response Type) in the subject of Mathematics..
More informationCBSE 2018 ANNUAL EXAMINATION DELHI
CBSE 08 ANNUAL EXAMINATION DELHI (Series SGN Code No 65/ : Delhi Region) Ma Marks : 00 Time Allowed : Hours SECTION A Q0 Find the value of tan cot ( ) Sol 5 5 tan cot ( ) tan tan cot cot 6 6 6 0 a Q0 If
More informationMarking Scheme (Mathematics XII )
Sr. No. Marking Scheme (Mathematics XII 07-8) Answer Section A., (, ) A A: (, ) A A: (,),(,) Mark(s). -5. a iˆ, b ˆj. (or an other correct answer). 6 6 ( ), () ( ) ( ). Hence, is not associative. Section
More informationAll Rights Reserved Wiley India Pvt. Ltd. 1
Question numbers to carry mark each. CBSE MATHEMATICS SECTION A. If R = {(, y) : + y = 8} is a relation of N, write the range of R. R = {(, y)! + y = 8} a relation of N. y = 8 y must be Integer So Can
More informationWBJEEM Answer Keys by Aakash Institute, Kolkata Centre MATHEMATICS
WBJEEM - 05 Answer Keys by, Kolkata Centre MATHEMATICS Q.No. μ β γ δ 0 B A A D 0 B A C A 0 B C A * 04 C B B C 05 D D B A 06 A A B C 07 A * C A 08 D C D A 09 C C A * 0 C B D D B C A A D A A B A C A B 4
More informationMATHEMATICS (SET -3) Labour cost Z 300x 400y (to be minimized) The constraints are: SECTION - A 1. f (x) is continuous at x 3 f (3) lim f (x)
8 Class th (SET -) BD PPER -7 M T H E M T I C S () SECTION -. f () is continuous at f () lim f () ( ) 6 k lim ( )( 6) k lim ( ) k. adj I 8 I 8 I 8I 8. P : z 5 5 P : 5 5z z 8 Distance between P & P sin
More informationOperating C 1 C 1 C 2 and C 2 C 2 C 3, we get = 0, as R 1 and R 3 are identical. Ans: 0
Q. Write the value of MATHEMATICS y y z z z y y y z z z y Operating R R + R, we get y z y z z y z y ( y z) z y Operating C C C and C C C, we get 0 0 0 0 ( y z) z y y ( y z)( ) z y y 0 0 0 0 = 0, as R and
More informationJEE MAIN 2013 Mathematics
JEE MAIN 01 Mathematics 1. The circle passing through (1, ) and touching the axis of x at (, 0) also passes through the point (1) (, 5) () (5, ) () (, 5) (4) ( 5, ) The equation of the circle due to point
More informationC.B.S.E Class XII Delhi & Outside Delhi Sets
SOLVED PAPER With CBSE Marking Scheme C.B.S.E. 8 Class XII Delhi & Outside Delhi Sets Mathematics Time : Hours Ma. Marks : General Instructions : (i) All questions are compulsory. (ii) The question paper
More informationCLASS XII MATHEMATICS. Weightage (Marks) (i) Relations and Functions 10. Type of Questions Weightage of Number of Total Marks each question questions
CLASS XII MATHEMATICS Units Weightage (Marks) (i) Relations and Functions 0 (ii) Algebra (Matrices and Determinants) (iii) Calculus 44 (iv) Vector and Three dimensional Geometry 7 (v) Linear Programming
More informationSET-I SECTION A SECTION B. General Instructions. Time : 3 hours Max. Marks : 100
General Instructions. All questions are compulsor.. This question paper contains 9 questions.. Questions - in Section A are ver short answer tpe questions carring mark each.. Questions 5- in Section B
More information02. If (x, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) x + y = 0 (B) bx ay = 0 (C) ax by = 0 (D) bx + ay = 0 (E) ax + by =
0. π/ sin d 0 sin + cos (A) 0 (B) π (C) 3 π / (D) π / (E) π /4 0. If (, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) + y = 0 (B) b ay = 0 (C) a by = 0 (D) b + ay = 0 (E) a + by = 0 03.
More informationRao IIT Academy/ SSC - Board Exam 2018 / Mathematics Code-A / QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS SSC - BOARD
Rao IIT cademy/ SSC - oard Exam 018 / Mathematics Code- / QP + Solutions JEE MEDICL-UG ORDS KVPY NTSE OLYMPIDS SSC - ORD - 018 Date: 1.0.018 MTHEMTICS - PPER- - SOLUTIONS Q.1 ttempt any FIVE of the following
More informationRao IIT Academy/ ICSE - Board 2018_Std X_Maths_QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS. X - ICSE Board MATHS - QP + SOLUTIONS
Rao IIT Academy/ ICSE - Board 018_Std X_Maths_QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS X - ICSE Board Date: 7.0.018 MATHS - QP + SOLUTIONS SECTION - A (40 Marks) Attempt all questions from
More informationPART B MATHEMATICS (2) (4) = +
JEE (MAIN)--CMP - PAR B MAHEMAICS. he circle passing through (, ) and touching the axis of x at (, ) also passes through the point () (, ) () (, ) () (, ) (4) (, ) Sol. () (x ) + y + λy = he circle passes
More informationMATHEMATICS. metres (D) metres (C)
MATHEMATICS. If is the root of the equation + k = 0, then what is the value of k? 9. Two striaght lines y = 0 and 6y 6 = 0 never intersect intersect at a single point intersect at infinite number of points
More informationHALF SYLLABUS TEST. Topics : Ch 01 to Ch 08
Ma Marks : Topics : Ch to Ch 8 HALF SYLLABUS TEST Time : Minutes General instructions : (i) All questions are compulsory (ii) Please check that this question paper contains 9 questions (iii) Questions
More informationMATHEMATICS SOLUTION
MATHEMATICS SOLUTION MHT-CET 6 (MATHEMATICS). (A) 5 0 55 5 9 6 5 9. (A) If the school bus does not come) (I will not go to school) ( I shall meet my friend) (I shall go out for a movie) ~ p ~ q r s ~ p
More informationMATHEMATICS (SET -1)
8 Class th (SET ) BD PPER -7 M T H E M T I C S (). adj 8 I 8 I 8I 8 SECTION - I. f () is continuous at f () lim f () ( ) 6 k lim ( )( 6) k lim ( ) k sin cos d tan cot d sin cos ln sec ln sin C.. P : z
More informationGOVERNMENT OF KARNATAKA KARNATAKA STATE PRE-UNIVERSITY EDUCATION EXAMINATION BOARD SCHEME OF VALUATION. Subject : MATHEMATICS Subject Code : 35
GOVERNMENT OF KARNATAKA KARNATAKA STATE PRE-UNIVERSITY EDUCATION EXAMINATION BOARD II YEAR PUC EXAMINATION MARCH APRIL 0 SCHEME OF VALUATION Subject : MATHEMATICS Subject Code : 5 PART A Write the prime
More informationSOLUTION CLASS-XII / (CBSE)
CBSE XII EXAMINATION-6 SOLUTION--6 CBSE th Board MATHEMATICS SET- CLASS-XII / CBSE Corporate Office : CG Tower, A-6 &, IPIA, Near Cit Mall, Jhalawar Road, Kota Raj.- PCCP Head Office: J-, Jawahar Nagar,
More informationFILL THE ANSWER HERE
HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP. If A, B & C are matrices of order such that A =, B = 9, C =, then (AC) is equal to - (A) 8 6. The length of the sub-tangent to the curve y = (A) 8 0 0 8 ( ) 5 5
More informationComplete Syllabus of Class XI & XII
Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-0005 Ph.: 0-7656 Fa : 0-767 MM : 0 Sample Paper : Campus Recruitment Test Time : ½ Hr. Mathematics (Engineering) Complete Syllabus of Class XI & XII
More information(iii) For each question in Section III, you will be awarded 4 Marks if you darken only the bubble corresponding to the
FIITJEE Solutions to IIT - JEE 8 (Paper, Code 4) Time: hours M. Marks: 4 Note: (i) The question paper consists of parts (Part I : Mathematics, Part II : Physics, Part III : Chemistry). Each part has 4
More informationMULTIPLE CHOICE QUESTIONS SUBJECT : MATHEMATICS Duration : Two Hours Maximum Marks : 100. [ Q. 1 to 60 carry one mark each ] A. 0 B. 1 C. 2 D.
M 68 MULTIPLE CHOICE QUESTIONS SUBJECT : MATHEMATICS Duration : Two Hours Maimum Marks : [ Q. to 6 carry one mark each ]. If sin sin sin y z, then the value of 9 y 9 z 9 9 y 9 z 9 A. B. C. D. is equal
More informationDIRECTORATE OF EDUCATION GOVT. OF NCT OF DELHI
456789045678904567890456789045678904567890456789045678904567890456789045678904567890 456789045678904567890456789045678904567890456789045678904567890456789045678904567890 QUESTION BANK 456789045678904567890456789045678904567890456789045678904567890456789045678904567890
More informationQUESTION BOOKLET 2016 Subject : Paper III : Mathematics
QUESTION BOOKLET 06 Subject : Paper III : Mathematics ** Question Booklet Version Roll No. Question Booklet Sr. No. (Write this number on your Answer Sheet) Answer Sheet No. (Write this number on your
More informationQUESTION BOOKLET 2016 Subject : Paper III : Mathematics
QUESTION BOOKLET 06 Subject : Paper III : Mathematics ** Question Booklet Version Roll No. Question Booklet Sr. No. (Write this number on your Answer Sheet) Answer Sheet No. (Write this number on your
More informationQUESTION BOOKLET 2016 Subject : Paper III : Mathematics
QUESTION BOOKLET 06 Subject : Paper III : Mathematics ** Question Booklet Version Roll No. Question Booklet Sr. No. (Write this number on your Answer Sheet) Answer Sheet No. (Write this number on your
More informationSTD. XII ISC - BOARD MATHEMATICS - SOLUTIONS
Rao IIT Academ/XII-ISC-Board -05_Mathematics_SOLUTIONS Date: 6.0.05 Question STD. XII ISC - BOARD MATHEMATICS - SOLUTIONS SECTION A (i) 4 6 M 6 4 9 5 8 M 8 km k k k k M km I 0 5 8 k k 0 0 0 8 k k 0 0 0
More informationSAMPLE QUESTION PAPER MATHEMATICS (041) CLASS XII
SAMPLE QUESTION PAPER MATHEMATICS (01) CLASS XII 017-18 Time allowed: hours Maimum Marks: 100 General Instructions: (i) All questions are compulsory. (ii) This question paper contains 9 questions. (iii)
More informationCBSE Mathematics 2016 Solved paper for Class XII(10+2) Section - A. Q. 1 For what value of k, the system of linear equations.
A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH CBSE Mathematics 06 Solved paper for Class XII(0+) Section - A Q. For what value of k, the system of linear equations. y z y z
More informationMINIMUM PROGRAMME FOR AISSCE
KENDRIYA VIDYALAYA DANAPUR CANTT MINIMUM PROGRAMME FOR AISSCE 8 SUBJECT : MATHEMATICS (CLASS XII) Prepared By : K. N. P. Singh Vice-Principal K.V. Danapur Cantt () MATRIX. Find X and Y if 7 y & y 7 8 X,,
More information2016 SEC 4 ADDITIONAL MATHEMATICS CW & HW
FEB EXAM 06 SEC 4 ADDITIONAL MATHEMATICS CW & HW Find the values of k for which the line y 6 is a tangent to the curve k 7 y. Find also the coordinates of the point at which this tangent touches the curve.
More informationMarking Scheme. Section A 3. 2 [1] l m n 1 n 1 cos [1] Direction ratios of the given line are 2, 1, 2.
Marking Scheme Section A. B. AB 6 A B 6. sin( ) cos( ) or sin( ). 4. l m n n cos 45 or 6 4 OR Direction ratios of the given line are,,. [/] Hence, direction cosines of the line are:,, or,, [/] Section
More informationSample Paper-05 Mathematics Class XII. Time allowed: 3 hours Answers Maximum Marks: 100. Section A. Section B
Sample Paper-05 Mathematics Class XII Time allowed: hours Answers Maimum Marks: 00. No. (, ) R but (, ) R r. a () + ( ) + ( 5) 8 5 l, m, n 8 8 8. [0, ]. A A ( 8) 8 ( 6) A 8 Hence Prove tan cos sin sin
More informationoo ks. co m w w w.s ur ab For Order : orders@surabooks.com Ph: 960075757 / 84000 http://www.trbtnpsc.com/07/08/th-eam-model-question-papers-download.html Model Question Papers Based on Scheme of Eamination
More informationMODEL PAPER - I MATHEMATICS. Time allowed : 3 hours Maximum marks : 100
MODEL PAPER - I MATHEMATICS Time allowed : 3 hours Maimum marks : General Instructions. All questions are compulsy.. The question paper consists of 9 questions divided into three sections A, B and C. Section
More informationANNUAL EXAMINATION - ANSWER KEY II PUC - MATHEMATICS PART - A
. LCM of and 6 8. -cosec ( ) -. π a a A a a. A A A A 8 8 6 5. 6. sin d ANNUAL EXAMINATION - ANSWER KEY -7 + d + + C II PUC - MATHEMATICS PART - A 7. or more vectors are said to be collinear vectors if
More information63487 [Q. Booklet Number]
WBJEE - 0 (Answers & Hints) 687 [Q. Booklet Number] Regd. Office : Aakash Tower, Plot No., Sector-, Dwarka, New Delhi-0075 Ph. : 0-7656 Fa : 0-767 ANSWERS & HINTS for WBJEE - 0 by & Aakash IIT-JEE MULTIPLE
More informationObjective Mathematics
Chapter No - ( Area Bounded by Curves ). Normal at (, ) is given by : y y. f ( ) or f ( ). Area d ()() 7 Square units. Area (8)() 6 dy. ( ) d y c or f ( ) c f () c f ( ) As shown in figure, point P is
More informationCHAPTER 10 VECTORS POINTS TO REMEMBER
For more important questions visit : www4onocom CHAPTER 10 VECTORS POINTS TO REMEMBER A quantity that has magnitude as well as direction is called a vector It is denoted by a directed line segment Two
More informationModel Answer Paper 24(24 1) 2 12
ICSE X SUBJECT : MATHEMATICS Marks : 80 Exam No. : MT/ICSE/Semi Prelim II- Set-B-00 Model Answer Paper Time : ½ hrs. SECTION I (40 Marks) A. (a) Maturity value ` 0,000 No. of months (n) 4 months Rate of
More informationQUESTION BOOKLET 2016 Subject : Paper III : Mathematics
QUESTION BOOKLET 06 Subject : Paper III : Mathematics ** Question Booklet Version Roll No. Question Booklet Sr. No. (Write this number on your Answer Sheet) Answer Sheet No. (Write this number on your
More informationCBSE MATHS 2010 YEAR PAPER
CBSE MATHS YEAR PAPER Important Instructions: (i) The question papers consists of three sections A B and C. (ii) All questions are compulsory. (iii) Internal choices have been provided in some questions.
More information12 th Class Mathematics Paper
th Class Mathematics Paper Maimum Time: hours Maimum Marks: 00 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 9 questions divided into four sections A, B, C
More informationPAPER ¼isij½- 1. SECTION-1 (Maximum Marks : 24)
JEE (Advanced) (ADVANCED) 06 08 PAPER ¼isij½- -05-06 DATE: 0-05-08 This question paper has three (0) parts: PART-I: Physics, PART-II: Chemistry and PART-III: Mathematics. Each part has total of eighteen
More informationMATHEMATICS. Time allowed : 3 hours Maximum Marks: 100
MATHEMATICS Time allowed : 3 hours Maimum Marks: 00 General Instructions:. All questions are compulsory.. This question paper contains 9 questions. 3. Questions 4 in Section A are very short-answer type
More informationCBSE Examination Paper, Foreign-2014
CBSE Eamination Paper, Foreign-4 Time allowed: hours Maimum marks: General Instructions: As per given in CBSE Eamination Paper Delhi-4. SET I SECTION A Question numbers to carr mark each.. Let R = {(a,
More information1 are perpendicular to each other then, find. Q06. If the lines x 1 z 3 and x 2 y 5 z
Useful for CBSE Board Examination of Math (XII) for 6 For more stuffs on Maths, please visit : www.theopgupta.com Time Allowed : 8 Minutes Max. Marks : SECTION A 3 Q. Evaluate : sin cos 5. Q. State the
More informationCBSE Examination Papers
CBSE Eamination Papers (Foreign 0) Time allowed: hours Maimum marks: 00 General Instructions: As given in CBSE Sample Question Paper. Set I SECTION A Question numbers to 0 carry mark each.. Write the principal
More informationDesign of Question Paper Mathematics - Class XII
Design of Question Paper Mathematics - Class XII Time : 3 hours Max. Marks : 100 Weightage of marks over different dimensions of the question paper shall be as follows : A. Weightage to different topics/content
More informationANSWER KEY 1. [A] 2. [C] 3. [B] 4. [B] 5. [C] 6. [A] 7. [B] 8. [C] 9. [A] 10. [A] 11. [D] 12. [A] 13. [D] 14. [C] 15. [B] 16. [C] 17. [D] 18.
ANSWER KEY. [A]. [C]. [B] 4. [B] 5. [C] 6. [A] 7. [B] 8. [C] 9. [A]. [A]. [D]. [A]. [D] 4. [C] 5. [B] 6. [C] 7. [D] 8. [B] 9. [C]. [C]. [D]. [A]. [B] 4. [D] 5. [A] 6. [D] 7. [B] 8. [D] 9. [D]. [B]. [A].
More informationAnswer. Find the gradient of the curve y x at x 4
(ISO/IEC - 7-5 Certified) SUMMER 8 EXAMINATION ject Name: Applied Mathematics Model wer ject Code: Important Instructions to eaminers: ) The answers should be eamined by key words and not as word-to-word
More information2 nd ORDER O.D.E.s SUBSTITUTIONS
nd ORDER O.D.E.s SUBSTITUTIONS Question 1 (***+) d y y 8y + 16y = d d d, y 0, Find the general solution of the above differential equation by using the transformation equation t = y. Give the answer in
More informationTime allowed : 3 hours Maximum Marks : 100
CBSE XII EXAMINATION-8 Series SGN SET- Roll No. Candiates must write code on the title page of the answer book Please check that this question paper contains printed pages. Code number given on the right
More informationMATHEMATICS. IMPORTANT FORMULAE AND CONCEPTS for. Final Revision CLASS XII CHAPTER WISE CONCEPTS, FORMULAS FOR QUICK REVISION.
MATHEMATICS IMPORTANT FORMULAE AND CONCEPTS for Final Revision CLASS XII 2016 17 CHAPTER WISE CONCEPTS, FORMULAS FOR QUICK REVISION Prepared by M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold Medallist (Elect.),
More informationIIT JEE (2012) (Calculus)
L.K. Gupta (Mathematic Classes) www.pioneermathematics.com MOBILE: 985577, 4677 PAPER B IIT JEE (0) (Calculus) TOWARDS IIT JEE IS NOT A JOURNEY, IT S A BATTLE, ONLY THE TOUGHEST WILL SURVIVE TIME: 60 MINS
More informationMT - GEOMETRY - SEMI PRELIM - I : PAPER - 4
07 00 MT A.. Attempt ANY FIVE of the following : (i) Slope of the line (m) 4 y intercept of the line (c) 0 By slope intercept form, The equation of the line is y m + c y (4) + (0) y 4 MT - GEOMETRY - SEMI
More informationMathematics. Guess Paper: 2014 Class: XII. Time Allowed: 3Hours Maximum Marks: 70. Section A
Mathematics Guess Paper: 04 Class: XII Time llowed: Hours Maimum Marks: 70 General Instructions:. The question paper consists of 9 questions divided into three sections, B and C.. Section comprises of
More informationQUESTION BANK. Class : 10+1 & (Mathematics)
QUESTION BANK Class : + & + (Mathematics) Question Bank for + and + students for the subject of Mathematics is hereby given for the practice. While preparing the questionnaire, emphasis is given on the
More informationMODEL TEST PAPER I. Time : 3 hours Maximum Marks : 100
MODEL TEST PAPER I Time : 3 hours Maimum Marks : 00 General Instructions : (i) (ii) (iii) (iv) (v) All questions are compulsory. Q. to Q. 0 of Section A are of mark each. Q. to Q. of Section B are of 4
More informationMAHARASHTRA STATE BOARD OF TECHNICAL EDUCATION (Autonomous) (ISO/IEC Certified)
SUMMER 8 EXAMINATION Important Instructions to eaminers: ) The answers should be eamined by key words and not as word-to-word as given in the model answer scheme. ) The model answer and the answer written
More informationMathematics Class X Board Paper 2011
Mathematics Class X Board Paper Solution Section - A (4 Marks) Soln.. (a). Here, p(x) = x + x kx + For (x-) to be the factor of p(x) = x + x kx + P () = Thus, () + () k() + = 8 + 8 - k + = k = Thus p(x)
More informationMATHEMATICS. r Statement I Statement II p q ~p ~q ~p q q p ~(p ~q) F F T T F F T F T T F T T F T F F T T T F T T F F F T T
MATHEMATICS Directions : Questions number to 5 are Assertion-Reason type questions. Each of these questions contains two statements : Statement- (Assertion) and Statement- (Reason). Each of these questions
More informationKEAM (ENGINEERING) ANSWER KEY 2017
MTHMTICS KM KY 07 PG: KM (NGINRING) KY 07 PPR II MTHMTICS QUSTIONS & S. p q r p q r + is equal to () q p () q + p (C) q () p () 0 5 0. Let = 0 5 5 () 0 and () 0 = 0. If + 5 C = 0, then C is 0 5 5 5 5 0
More informationMathematics. Section B. CBSE XII Mathematics 2012 Solution (SET 2) General Instructions:
CBSE XII Mathematics 0 Solution (SET ) General Instructions: Mathematics (i) (ii) (iii) (iv) (v) All questions are compulsor. The question paper consists of 9 questions divided into three Sections A, B
More informationIIT-JEE (2012) (Vector+3D+Probability) Solutions
L.K. Gupta (Mathematic Classes) www.pioneermathematics.com MOBILE: 985577, 4677 PAPER -A IIT-JEE (0) (Vector+D+Probability) Solutions TOWARDS IIT- JEE IS NOT A JOURNEY, IT S A BATTLE, ONLY THE TOUGHEST
More informationJEE (Advanced) 2018 MATHEMATICS QUESTION BANK
JEE (Advanced) 08 MATHEMATICS QUESTION BANK Ans. A [ : a multiple of ] and B [ : a multiple of 5], then A B ( A means complement of A) A B A B A B A B A { : 5 0}, B {, }, C {,5}, then A ( B C) {(, ), (,
More informationMATHEMATICS Class: XII Mock Paper 1 Solutions
MATHEMATICS Class: XII Mock Paper Solutions Section A. If A { a, b, c } and B {,, } and a function f : A B is given by f { (a, ), ( b, ), ( c, ) } Every element of set A is mapped to the unique element
More informationSOLUTIONS TO CONCEPTS CHAPTER 2
SOLUTIONS TO CONCPTS CHAPTR 1. As shown in the figure, The angle between A and B = 11 = 9 A = and B = 4m Resultant R = A B ABcos = 5 m Let be the angle between R and A 4 sin9 = tan 1 = tan 1 (4/) = 5 4cos9
More informationAnswers for NSSH exam paper 2 type of questions, based on the syllabus part 2 (includes 16)
Answers for NSSH eam paper type of questions, based on the syllabus part (includes 6) Section Integration dy 6 6. (a) Integrate with respect to : d y c ( )d or d The curve passes through P(,) so = 6/ +
More information3. Total number of functions from the set A to set B is n. 4. Total number of one-one functions from the set A to set B is n Pm
ASSIGNMENT CLASS XII RELATIONS AND FUNCTIONS Important Formulas If A and B are finite sets containing m and n elements, then Total number of relations from the set A to set B is mn Total number of relations
More informationEINSTEIN CLASSES. C B S E XIIth Board PRACTICE ASSIGNMENT
EINSTEIN CLASSES P R E S E N T S C B S E XIIth Board PRACTICE ASSIGNMENT MATHEMATICS NOTE THE FOLLOWING POINTS : Einstein Classes is primarily concerned with the preparation of JEE-ADVANCE /JEE-MAIN/BITS/PMT/AIIMS
More informationRegn. No. North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-09, Ph: ,
1. Section-A contains 0 Multiple Choice Questions (MCQ). Each question has 4 choices (a), (b), (c) and (d), for its answer, out of which ONLY ONE is correct. From Q.1 to Q.10 carries 1 Marks and Q.11 to
More informationPaper: 02 Class-X-Math: Summative Assessment - I
1 P a g e Paper: 02 Class-X-Math: Summative Assessment - I Total marks of the paper: 90 Total time of the paper: 3.5 hrs Questions: 1] The relation connecting the measures of central tendencies is [Marks:1]
More informationSaturday, March 27, :59 PM Annexure 'F' Unfiled Notes Page 1
Annexure 'F' CLASS-XII SAMPLE QUESTION PAPER MATHEMATICS CLASS XII (2013-14) BLUE PRINT Unit VSA (1) SA (4) LA (6) Total I. Relations and Functions 1 (1) 4 (1) 5 (2) Inverse Trigonometric Functions
More informationSAMPLE QUESTION PAPER MATHEMATICS CLASS XII ( ) BLUE PRINT. Unit VSA (1) SA (4) LA (6) Total. I. Relations and Functions 1 (1) 4 (1) 5 (2)
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII (2013-14) BLUE PRINT Unit VSA (1) SA (4) LA (6) Total I. Relations and Functions 1 (1) 4 (1) 5 (2) Inverse Trigonometric Functions 1 (1) *4 (1) 5 (2) II. Matrices
More informationSECTION A 1. Find the vector equation of a plane which is at a distance of 5 units from the origin and its normal vector is 2iˆ
Session: 01-17 Subject: Mathematics Class XII Duration: 3 hr. M.M: 100 General Instructions: (i) All questions are compulsor. (ii) This question paper contains 9 questions. (iii) Question 1 in Section
More information1969 AP Calculus BC: Section I
969 AP Calculus BC: Section I 9 Minutes No Calculator Note: In this eamination, ln denotes the natural logarithm of (that is, logarithm to the base e).. t The asymptotes of the graph of the parametric
More information1985 AP Calculus AB: Section I
985 AP Calculus AB: Section I 9 Minutes No Calculator Notes: () In this eamination, ln denotes the natural logarithm of (that is, logarithm to the base e). () Unless otherwise specified, the domain of
More informationRAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION / STD - VIII / QP + SOLUTIONS JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS GANIT PRABHUTWA EXAMINATION
JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS GANIT PRABHUTWA EXAMINATION Date : 0 - - 07 Std - VIII Total Marks : 00 Time : Hours Q. A) Choose the correct alternative and write it against the correct sub
More informationSummer Review Packet for Students Entering AP Calculus BC. Complex Fractions
Summer Review Packet for Students Entering AP Calculus BC Comple Fractions When simplifying comple fractions, multiply by a fraction equal to 1 which has a numerator and denominator composed of the common
More informationb = 2, c = 3, we get x = 0.3 for the positive root. Ans. (D) x 2-2x - 8 < 0, or (x - 4)(x + 2) < 0, Therefore -2 < x < 4 Ans. (C)
SAT II - Math Level 2 Test #02 Solution 1. The positive zero of y = x 2 + 2x is, to the nearest tenth, equal to (A) 0.8 (B) 0.7 + 1.1i (C) 0.7 (D) 0.3 (E) 2.2 ± Using Quadratic formula, x =, with a = 1,
More informationPreliminary Mathematics
NORTH SYDNEY GIRLS HIGH SCHOOL 010 YEARLY EXAMINATION Preliminary Mathematics General Instructions Reading Time 5 minutes Working Time hours Write using black or blue pen Board-approved calculators may
More information2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is
. If P(A) = x, P = 2x, P(A B) = 2, P ( A B) = 2 3, then the value of x is (A) 5 8 5 36 6 36 36 2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time
More informationWest Essex Regional School District. AP Calculus AB. Summer Packet
West Esse Regional School District AP Calculus AB Summer Packet 05-06 Calculus AB Calculus AB covers the equivalent of a one semester college calculus course. Our focus will be on differential and integral
More informationMATHEMATICS. Time allowed : 3 hours Maximum Marks : 100
MATHEMATICS Time allowed : hours Maimum Marks : General Instructions:. All questions are compulsory.. The question paper consists of 9 questions divided into three sections, A, B and C. Section A comprises
More informationCBSE Board Paper Class-XII. Time allowed : 3 hours Maximum Marks : 100
L.K.Gupta (Mathematic Classes) www.poineermathematics.com. MOBILE: 98155771, 461771 CBSE Board Paper -011 Class-XII (SET-1) Time allowed : hours Maimum Marks : 100 General Instructions: (i) All questions
More informationMemory Based Questions & Solutions
PAPER- (B.E./B. TECH.) JEE (Main) 09 COMPUTER BASED TEST (CBT) Memory Based Questions & Solutions Date: 09 April, 09 (SHIFT-) TIME : (9.0 a.m. to.0 p.m) Duration: Hours Ma. Marks: 60 SUBJECT : MATHEMATICS
More informationMATHEMATICS. MINIMUM LEVEL MATERIAL for CLASS XII Project Planned By. Honourable Shri D. Manivannan Deputy Commissioner,KVS RO Hyderabad
MATHEMATICS MINIMUM LEVEL MATERIAL for CLASS XII 06 7 Project Planned By Honourable Shri D. Manivannan Deputy Commissioner,KVS RO Hyderabad Prepared by M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold Medallist
More information1 / 23
CBSE-XII-07 EXAMINATION CBSE-X-009 EXAMINATION MATHEMATICS Series: HRL Paper & Solution Code: 0/ Time: Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question paper
More informationMaharashtra Board Class XII - Mathematics & Statistics Board Question Paper 2016 (ARTS & SCIENCE) Time: 3 hrs Max. Marks: 80 SECTION I
Maharashtra Board Class XII - Mathematics & Statistics Board Question Paper 016 (ARTS & SCIENCE) Time: 3 hrs Ma. Marks: 80 SECTION I 1. (A) Select and write the most appropriate answer from the given [1]
More informationQUESTION PAPER CODE 65/2/2/F EXPECTED ANSWER/VALUE POINTS
QUESTION PAPER CODE EXPECTED ANSWER/VALUE POINTS SECTION A. P 6 (A A ) P 6 9. (a b c) (a b c) 0 a b c (a b b c c a) 0 a b b c c a. a b sin θ a b cos θ 400 b 4 4. x z 5 or x z 5 mark for dc's of normal
More informationNATIONAL QUALIFICATIONS
Mathematics Higher Prelim Eamination 04/05 Paper Assessing Units & + Vectors NATIONAL QUALIFICATIONS Time allowed - hour 0 minutes Read carefully Calculators may NOT be used in this paper. Section A -
More information